WASHINGTON, Nov. 27 — A senior American intelligence official said Monday that the Iranian-backed group Hezbollah had been training members of the Mahdi Army, the Iraqi Shiite militia led by Moktada al-Sadr.

The official said that 1,000 to 2,000 fighters from the Mahdi Army and other Shiite militias had been trained by Hezbollah in Lebanon. A small number of Hezbollah operatives have also visited Iraq to help with training, the official said.

Iran has facilitated the link between Hezbollah and the Shiite militias in Iraq, the official said. Syrian officials have also cooperated, though there is debate about whether it has the blessing of the senior leaders in Syria.

The intelligence official spoke on condition of anonymity under rules set by his agency, and discussed Iran’s role in response to questions from a reporter.

The interview occurred at a time of intense debate over whether the United States should enlist Iran’s help in stabilizing Iraq. The Iraq Study Group, directed by James A. Baker III, a former Republican secretary of state, and Lee H. Hamilton, a former Democratic lawmaker, is expected to call for direct talks with Tehran.

The claim about Hezbollah’s role in training Shiite militias could strengthen the hand of those in the Bush administration who oppose a major new diplomatic involvement with Iran.

The new American account is consistent with a claim made in Iraq this summer by a mid-level Mahdi commander, who said his militia had sent 300 fighters to Lebanon, ostensibly to fight alongside Hezbollah. “They are the best-trained fighters in the Mahdi Army,” he said, speaking on condition of anonymity.

The specific assertions about Iran’s role went beyond those made publicly by senior American officials, though Gen. Michael V. Hayden, the director of the Central Intelligence Agency, did tell Congress this month that “the Iranian hand is stoking violence” in Iraq.

The American intelligence on Hezbollah was based on human sources, electronic means and interviews with detainees captured in Iraq.

American officials say the Iranians have also provided direct support to Shiite militias in Iraq, including explosives and trigger devices for roadside bombs, and training for several thousand fighters, mostly in Iran. The training is carried out by the Iranian Revolutionary Guards and the Ministry of Intelligence and Security, they say.

In Congressional testimony this month, General Hayden said he was initially skeptical of reports of Iran’s role but changed his mind after reviewing intelligence reports.

“I’ll admit personally,” he said at one point in the hearing, “that I have come late to this conclusion, but I have all the zeal of a convert as to the ill effect that the Iranians are having on the situation in Iraq.”

Lt. Gen. Michael D. Maples, the director of the Defense Intelligence Agency, offered a similar assessment in his testimony.

Neither General Hayden nor General Maples described Hezbollah’s role during the hearing.

In the interview on Monday, the senior intelligence official was asked for further details about the purported Iranian role.

“They have been a link to Lebanese Hezbollah and have helped facilitate Hezbollah training inside of Iraq, but more importantly Jaish al-Mahdi members going to Lebanon,” the official said, describing Iran’s role and using the Arabic name for the Mahdi Army.

The official said the Hezbollah training had been conducted with the knowledge of Mr. Sadr, the most influential Shiite cleric.

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While Iran wants a stable Iraq, the official said, it sees an advantage in “managed instability in the near term” to bog down the American military and defeat the Bush administration’s objectives in the region.

“There seems to have been a strategic decision taken sometime over late winter or early spring by Damascus, Tehran, along with their partners in Lebanese Hezbollah, to provide more support to Sadr to increase pressure on the U.S.,” the American intelligence official said.

Some Middle East experts were skeptical about the assessment of Hezbollah’s training role.

“That sound to me a little bit strained,” said Flynt Leverett, a senior fellow at the New America Foundation and a Middle East expert formerly on the National Security Council staff. “I have a hard time thinking it is a really significant piece of what we are seeing play out on the ground with the various Shiite militia forces.”

But other specialists found the assessment plausible. “I think it is plausible because Hezbollah is the best in the business, and it enhances their position with Iran, Syria and Iraq,” said Judith Kipper, of the Council on Foreign Relations.

The Mahdi Army and other militia fighters traveled to Lebanon in groups of 15 and 20 and some were present during the fighting between Hezbollah and Israel this summer, though there was no indication they had taken part in the fighting, the American intelligence official said.

Asked what the militia members had learned, the official replied, “Weapons, bomb-making, intelligence, assassinations, the gambit of skill sets.”

There is intelligence that indicates that Iran shipped machine tools to Lebanon that could be used to make “shaped charges,” sophisticated explosive devices designed to penetrate armor, American officials have said. But it is not known how the equipment was in fact used.

The officials said that because the Iraqi militia members went through Syrian territory, at least some Syrian officials were complicit. There are also reports of meetings between Imad Mugniyah, a senior Hezbollah member; Ghassem Soleimani of the Iranian Revolutionary Guards; and Syrian representatives to discuss ways of stepping up the pressure on the United States in Iraq.

The mid-level Mahdi commander interviewed this summer said the group sent to Lebanon was called the Ali al-Hadi Brigade, named for one of two imams buried at the Askariya Mosque in Samarra. The bombing of that shrine in February unleashed the fury of Shiite militias and accelerated sectarian violence.

According to the Mahdi commander, the brigade was organized and dispatched by a senior Mahdi officer known as Abu Mujtaba. It went by bus to Syria in July, and was then led across the border into Lebanon, he said. He said the fighters were from Diwaniya and Basra, as well as from the Shiite neighborhoods of Shoala and Sadr City in Baghdad.

“They travel as normal people from Iraq to Syria,” one of the militiamen said. “Once they get to Syria, fighters in Syria take them in.”

Among American officials, concern over the purported Iranian, Syrian or Hezbollah role grew recently when an advanced antitank weapon, an RPG-29, was used against an American M-1 tank in Iraq.

“The first time we saw it was not in Iraq,” Gen. John P. Abizaid, the head of the United States Central Command, told reporters in September. “We saw it in Lebanon. So to me, No. 1, it indicates an Iranian connection.”

American intelligence officials said the source of the weapon was still unclear.

General Abizaid also said it was hard to pin down some details of relationships between armed factions in the Middle East, adding: “There are clearly links between Hezbollah training people in Iran to operate in Lebanon and also training people in Iran that are Shia splinter groups that could operate against us in Iraq These linkages exist, but it is very, very hard to pin down with precision.”